Python: Jenks Natural Breaks

This week we will talk about the Jenks Natural Breaks, it is mostly useful for determining the map ranges. It finds the best way to split the data into ranges, for example, if we have 50 countries, 15 countries with 0 - 3 values, 20 countries with values from 5 - 10, and 15 countries with 15 - 20. Therefore, if we want to plot them on a map with different colors, the best way we are splitting the data is 0-3, 3-10, and 10-20. The Jenks Natural Breaks is an algorithm that will figure this out by grouping the similar values into a group. Let’s see the example below. I am using an existing package - jenkspy, to calculate the breaks. You can find the notebook on Qingkai’s Github.

import jenkspy
import numpy as np
import matplotlib.pyplot as plt
plt.style.use('seaborn-poster')

%matplotlib inline

# Let's generate this 3 classes data
data = np.concatenate([np.random.randint(0, 4, 15), \
  np.random.randint(5, 11, 20), np.random.randint(15, 21, 15)])

# Let's calculate the breaks
breaks = jenkspy.jenks_breaks(data, nb_class=3)
breaks

[0.0, 3.0, 10.0, 20.0]

plt.figure(figsize = (10,8))
hist = plt.hist(data, bins=20, align='left', color='g')
for b in breaks:
    plt.vlines(b, ymin=0, ymax = max(hist[0]))

We could see the above figure that the breaks (black lines) are exactly what we expect!

How it works?

The method is an iterative process to repeatedly test different breaks in the dataset to determine which set of breaks has the smallest in-class variance. You can see the above figure that within each group/class, the variance is smallest. But note that if only minimize the in-class variance, if we maximize the out-class variance (that is variance between different groups), the breaks will fall into the middle of the gaps above figure (in this case, it will be 4.5, 12.5, but I didn’t try).

Another example

Let’s have fun and see what the breaks for a normal distribution. (I didn’t find the connection to 3 sigmas as I thought!).

np.random.seed(1)
normal = np.random.normal(loc=0.0, scale=1.0, size=500)

breaks = jenkspy.jenks_breaks(normal, nb_class=5)
breaks

[-2.79308500014654,
 -1.3057269225577375,
 -0.39675352685597737,
 0.386539145133091,
 1.2932258825322618,
 3.0308571123720305]

plt.figure(figsize = (10,8))
hist = plt.hist(normal, bins=20, align='left', color='g')
for b in breaks:
    plt.vlines(b, ymin=0, ymax = max(hist[0]))

References

What is the Jenks Natural Breaks?
Jenks natural breaks optimization - Wikipedia